Rainfall-runoff model for design flood computation with variable parameters
S. Ignar en J.J. Bogardi
RAPPORT 32 Februari 1993
Vakgroep Waterhuishouding Nieuwe Kanaal 11, 6709 PA Wageningen
ISSN 0926-230X
S?'f°S CONTENTS
1. Introduction 3
2.Descriptio no fth emode l 3
2.1.Genera lcomment s 3 2.2.Tota lrainfal levaluatio n 6 2.3.Effectiv erainfal lcalculatio n 9 2.4.Rainfal lrunof ftransformatio n 10
3.Practica lapplication san dconclusion s 12
3.1.Genera lcomment s 12 3.2.Verificatio no fcomputation s 12 3.3.Sensitivit yanalysi s 15 3.4.Simulatio nevaluatio no fprobabilit ycurve sfo r anthropogenicchange s 16 3.5.Conclusion s 19
References 20 1. INTRODUCTION
Analysis of development andmovemen to ffloo d flows is one of the most important subjects in hydrological research. Conducted investigations areaime d torecogniz eth eparticula r processes involved infloo d forming,thei rforma ldescriptio nan deffort st omode l them.A properlydevelope dmodel ,bein ga simplifie ddescriptio no fth erea lth e watershedssystem ,allow st odetermin ewatershe dreactio no nrainfal la s an input impulse. Modeling methodology makes also possible to investigate all changes, including antropogenic and climatic ones in the watershed, and their impact on flood flows. The main problem of mathematical modelingo fsmal lwatershed s- th elac ko f recorded data- can be overcomed by applying simple,conceptua l rainfall-runoff models withonl ya fe wparameters .Parameter so fthes emodel sca nb edetermine d from correlation formulae and topographic maps. Such models allow for usageo f the unit hydrographmetho d forcomputatio n of flood caused by estimated rainfall. The proposed model will be applied to four small catchmentsi nPoland .
2.DESCRIPTIO NO FTH EMODE L
2.1.GENERA LCOMMENT S
This report describes the investigation and development of a conceptualmode lfo rdesig nfloo devaluatio nwit hassume dprobabilit yo f occurrence. The proposed methodology isbase d on transformation of the rainfall with assumed probability of occurrence into flood hydrograph. It is a modified version of the conceptual model described by Ignar (1986). The original version of themode lconsist s of three sub-models leadingt oevaluatio nof : a) totalrainfal l- P b) effectiverainfal l- H c) directflo whydrograp h- Q It requires from the user the arbitrary assessment of different parameterset sfo rth ethre esub-models .Suc ha narbitrar yassessmen t is oftencriticize da si tdoe sno tensur eth eequalit yo fprobabilitie sfo r input rainfall and computed flood. It isbecaus ecalculate d flood with assumed probabilityca n be caused byon eo fman ypossibl e combinations ofrainfal ldepth ,tim edistributio nan dduratio nan darea lvariability . Tosolv ethes eproblem sa simulatio ntechniqu ei sproposed ,whic hallow s toappl yman yset so fsub-mode lparamete rvalue sfo rassume dprobabilit y distributions of these parameters (Beran 1973). The proposed technique consistso fth efollowin gstages : a)assumin go feven tprobability , b)rando mselectio no frainfal lduration , c)evaluatio no ftota l rainfalldept hfro mrelation sbetwee nth e aboveassume dprobability ,selecte dduratio nan ddept ho frainfall , d)assumin go ftim edistributio nfo rrainfall , e)selectio n ofC N parameter valuean d effective rainfall evaluation bySC Smethod , f)transformatio no feffectiv erainfal lint ofloo dflows , g)determinatio no fstatistica ldistributio nfo rcompute dfloods .
W CN °,/K
V P(%) X) W E Q,
i • 1 N
Figure 1.Mode l structure Input oi watershed data
Event probability specllicatlon
Selection ol rainlall duration
Total rainlall depth determination
Selection ol rainlall time distribution
Selection ol CN parameter value
Eilective rainlall evaluation by SCS method
Eilective ralnlall translormatlon Into llood hydrographs by UH method
NO
YES
Statistical distribution ol peak Hows determination
Figure 2. Flowchart ol the proposed procedure Stages from b to f will be repeated by a prespecified number of times and for each recurrence values of rainfall duration, depth, distribution and parameter for effective rainfall determination method will be evaluated by random number generator from assumed statistical distributions of these values. The parameters of the above mentioned probabilitydistribution swer ederive dfro mempirica ldata .Th epropose d modelstructur e isshow n infigur e1 an d itsflowchar t infigur e2 .Th e procedureha sbee nprogramme d inPASCA Llanguag efo rPC/A Tmicrocompute r asa modula rpackage .
2.2.TOTA LRAINFAL LEVALUATIO N
In order to describe the input rainfall characteristics for the proposed procedure, the probability of occurrence,duration , intensity and time distribution have to be determined. Design probabilities are assumed inaccordanc ewit hth eimportanc eo fth edesigne dstructur ean d range of damages caused by its possible failure. These probabilities fallwithi nth erang efro m0.1 %t o3 %fo rvariou sregulation s inPoland . Duration of rainfall is usually taken to be equal to the time of concentration for an analyzed watershed, assuming that it would cause thebigges tfloo d flow.Simulatio n computationso fflood shav eshown , thatthi sassumptio nwa sno tvali dfo rmos to fth ecase s (Banasik,Igna r 1986). Inth epropose dprocedur eth erainfal lduratio nwil l berandoml y takenfro mprobabilit ydistributio n inorde rt oavoi dthi sdisadvantage . The rainfall data recorded for Wadowice weather station in south part of Poland were analyzed. Eight years of hourly sums were tested takingint oaccoun tal lrainfall shighe rtha n5 m m (totalpe revent )an d lasting longer than3 hours. 179event s fulfilling these criteria were collected.Averag eduratio no f8 hour swit hth estandar ddeviatio nequa l to5. 6h wer eobtained .Th etransforme dvariable :
t'= (t- 2) 1/3 ...2.1
(wheret denote sth eobserve dstor mduration )ha sbee nfoun d tofi t the normaldistributio n function.Th eaverag evalu eo ft 'wa s 1.674 and the standarddeviatio nwa s0.502 . The mean intensity of total rainfall isdeterministicall y related to itsduratio n and probability. Sucha dependenc e can be described by thegenera l formula (Raudkivi1979) :
T ...2.2 (t+ c)n where: J- rainfal l intensity (mm/h), t- rainfal lduratio n(h) , T -retur nperio d (years), k,x,c,n- regiona lan dclimati ccoefficients .
Regional and climatic coefficients in formula 2.2 and its modificationsar edetermine dempiricall yb yusin grainfal l records.Fo r the proposed procedure the indirect method developed for Poland by Stachy (1976) was adopted. Rainfall intensity is evaluated by the equation:
J .= *(t )• P ...2.3 P.t P
where: Jp.t- rainfal l intensity (mm/h), p- rainfal lprobabilit y(%) , t- rainfal lduratio n(h) , P -dail ymaximu mrainfal lwit hprobabilit yp (mm) , *(t)- reductio nfunctio nvalu efo rduratio nt (1/h).
The reduction function form was developed by Stachy for Poland usingavailabl edata . Totalrainfal lintensit yi sno tconstan ti ntim ean d theofte nuse d rectangular rainfalldistributio nschem eca n lead to serious errors in computed flows.Ther ear equit ea loto f "typical"stor m distribution patterns shown in literature. All of them have been obtained from recorded data analysis. Rainfall distribution pattern described by dimensionlessmas scurv ewa sadopte dfo rth epropose dalgorith m (Ignar, Weglarczyk 1991).Suc ha mode lca nb eformulate da sfollows : for each total rainfall P (mm)wit h duration T (hour)an d mass curve h(ta)(mm )(t ae [0,T],h(0 )= 0 ,h(T )= P )i ti spossibl et odefin eb y equation 2.4 the rainfall dimensionlessmas scurv eh (ta ),wher e h e [0,1] is a dimensionless height of rainfall and ta c [0,1] is a dimensionlessrainfal lduration :
• * h(ta) h (ta )= 5— v ...2.4 * ta t = —
Therear efollowin gassumptio nt odefin ea model : 1.Eac h single rainfall event with heightan dduratio n normalized to unitca nb edescribe db ydeterministi cunimoda lfunctio nh (t;a,ß )a sa normalized incompletebet afunction :
* t *a- 1 *ß- 1 * h*(t*;a,ß)= (t ) L -(1- tT dt ...2.5 ß(a,ß) . 0 where: ß(a,ß)- Eule rbet afunction , h*(0)= 0 ,h*(l )= 1 , a> o ,ß > 0 - functio nparameters .
2.Parameter sa an dß infunctio n2. 5ar eprobabilisti cvariable sfro m general population (A, B) with probability distribution described by f ( The method foreffectiv e rainfall determination isa very important part ofan yrainfall-runof f modeling technique. Theeffectiv e rainfall H is defined asa part of total rainfall remaining after withdrawing of losses consisting of: infiltration, évapotranspiration, interceptionan d depression storage. Among theman y methods used inengineerin g hydrology the SCS(Soi l Conservation Service) Curve Number method wasadopte d in the proposed procedure. This method was fully described by SCS(NE H 1985). The depth of effective rainfall, H is subjected to theC N parameter depending on: soil type, land use, soil conservation practices and antecedent moisture conditions. This parameter is related toth e maximum retention,S i nmm : r 1000 -J' S =25. 4 - - 10 ...2. 6 L CN J and effective rainfall canb e calculated from the simple empirical formula: [P -0. 2- S 1 H= ..2.7 P+ 0. 8 -S where: P -tota lrainfal ldept h(mm) . Usingthi sformul ai ti spossibl et odetermin eth eeffectiv erainfal li n subsequent time intervals. The value of the CN parameter can be evaluated fromsoi lmap san dtable sdevelope db ySC S (NEH1985) . Variability of CN value for particular floods is caused mostly by differences in initial wetness of watershed and in SCS method it is taken into account bycalculatin g rainfall totals for fiveday sbefor e the analyzed flood. There are three levels of antecedent moisture conditions (AMC)an d itseem s to be not enough flexible for real life conditions. Hawkins et al (1985) proposed to apply a log-normal distributionwhic hca nb eadopte dfo rdescribin gth edistributio no fth e CN values according to different moisture conditions. Such a distribution was adopted for this proposed procedure for random evaluationo fC Nvalues . 2.4. RAINFALLRUNOF FTRANSFORMATIO N Among the many existing rainfall-runoff models the Wackermann conceptual model of two parallel cascades consisting of two linear reservoirswa sadopte dfo rrainfal l runoff transformation (Ignar 1986). Iti sa specia lcas eo fa mor egenera l Diskin (1964)model .Parameter s ofthes emode l(i .e .Kl ,K 2- retentio ncoefficient sfo rth efirs tan d second cascades, and ß - dividing coefficient for input effective rainfall)ca nb eevaluate d from theformula e developed byDVW K (1984) fromdat arecorde di nove r9 0watershed ssituate di nth ewester npar to f Germany. Available recorded data from 13 agricultural watershed in Polandwer ecollecte db yth eauthor sfo rth eWackerman nmode l parameter evaluationi norde rt ofin dsimila rempirica l formulae.Tota lnumbe ro f 60floo devent swer egathered ,wit ha t least3 fo reac hwatershed .Th e watershed description summary is shown in Table 1.Mode l parameters values were calculated byth eoptimizatio n method based onRosenbroc k technique.Correlatio n formulae similart othes e obtainedb yDVW K were developedfo roptimize dparamete rvalue susin gth eleas tsquare smethod : -0.403 ß =0.0 4 •f—— j ...2.8 0.159 Kl= 1.2 8- I—— I ...2.9 ^ 0.379 K2= 0.89 2.[—— 1 ...2.10 where: L- th ehorizonta lprojectio no fth echanne l lengthfro mth emos t distantpoin tt oth ebasi noutle t(km) , I- slop ebetwee nthes etw opoint s(-) . 10 Then, verification calculations were conducted with the use of independent data from 8 observed watersheds, listed in Table 2. 55 rainfall-runoff events for these watersheds were collected. The criterion proposed by Delleur et al. (1973), so-called special correlation coefficient (Rs)wa s used for comparison of observed and simulated hydrographs. The authors of the criterion determined five intervals making it possible to evaluate the agreement between the observed hydrographs and the one computed by the model, by using five grades from excellent (denoted by 5 to poor (denoted by 1).Thes e intervals are: 0.99 < Rs< 1. 0 excellent= 5 0.95 < Rs< 0.9 9 verygoo d= 4 0.90 < Rs< 0.9 5 good =3 0.85 < Rs< 0.9 0 fair =2 0.00 < Rs< 0.8 5 poor =1 There were: one very good grade, three good, one fair and three poor among 8 tested watersheds. Based on this evidence the derived formulaehav ebee nadopte dfo rpropose dmodel . Table1 .Optimize dWatershed sDescriptio nSummar y Area Channel Levels No WATERSHED Profile length difference km2 km m 1 Zago2d2onka Wygoda 9.3 6.6 14.0 2 CzarnaWod a Jaworki 11.7 9.4 702.0 3 MlawaI I Uniszki 18.2 5.0 31.0 4 Lesnianka Lipowa 21.5 6.2 628.0 5 Trzeburika Stróza 30.4 10.7 563.0 6 Bobr Bukówka 58.5 9.4 599.0 7 Wisla Ustron 108.2 20.3 820.0 8 Bolszewka Bolszewo 221.1 25.9 90.3 9 Wilga Oziemkówka 231.6 23.6 59.0 10 Skawa Osielec 239.7 37.1 973.0 11 Sola Rajcza 254.0 16.8 840.0 12 NysaKlodzk a Bystrzyca 260.2 34.6 1084.0 13 Lososina Jakubkowice 342.6 49.4 922.0 11 Table2 .Verificatio nCalculation sSummar y Area Channel Levels No WATERSHED Profile length difference RS grade km2 km m 1 MlawkaI V Uniszki 35.5 5.35 31.7 0.460 1 2 Moszczeniczka Pieszcz 67.7 15.90 42.0 0.979 4 3 Skierniewka Boryslaw 98.2 17.30 48.9 0.900 3 4 Swislina Rzepin 118.0 28.20 152.9 0.919 3 5 CzarnaOraw a Jablonka 136.0 24.30 328.0 0.794 1 6 Raba MszanaDin . 161.7 30.00 599.4 0.770 1 7 Mszanka MszanaDin . 174.6 15.60 939.2 0.872 2 8 Kwisa Mirsk 185.6 19.70 785.0 0.902 3 3.PRACTICA LAPPLICATION SAN DCONCLUSION S 3.1.GENERA LCOMMENT S Verificationo fa mode l ison eo fth emos t important stagesi nth e modeldevelopin gprocess .I tallow sfo revaluatin g themode lqualit yb y comparing actual watershed output with model output,an dfo rassessin g thepractica lapplicabilit yo fhydrologica lcomputations . Verification of the model was conducted by comparison of empirically calculated probability curves with simulated ones. A sensitivity analysis was also performed, accompanied by a simulation calculationfo ranthropogeni c influenceso nfloo dflows . 3.2.VERIFICATIO NO FCOMPUTATION S Verification of computations have been conducted for four small basins located in the Carpatian Mountains. Table 3 shows the basic information concerning the basins. Empirical probability curves were developed bya standar d statistical method assuming a Pearson typeII I distribution. Developed curves are shown in figures 3 to 6, together 12 0 fa3/sl 30 ,_ ., pmpiriral riirvp simulated curve / . />' confidence limits /y _ _^.__ // / / / y' a K/\ _---^ ^^ w ^^ *\\ .^ 0 __i_ j—i—i— «0 SS 90 80 70 60 50 40 30 20 70 5 2 7 Q5 p/%; Q2 • Q7 Figure 3. Comparison of probability curves for river Lesnianka profile Lipowa hi 70 / 60 empirical curve / / simulated curve / 50 confidence limits / / y / / 10 ' y^ y* y 30 y' y . _.--- -•— — ^^' 20 / ^^ y ^" y' 70 y"^ 0 i i i i ' ' • • ,,,, • ' • • • ' I . K» 99 90 80 70 60501030 20 » 5 2 7 Q5 p/%; Q2 07 Figure 4. Comparison of probability curves for river Lubienka profile Lubien 13 90 Q / / / / / empiricalcurv e / / y / y 70 simulated curve / / / confidence limits / / / / 60 / S / / / S S / y /{/' y 50 / s y y // y / y / z ' Iß ' y / / y / y • / . ' y 30 / /. 7 , ' y 20 • ' • • • • • ,' • i' l L— 1 1 . 100 99 9080 70 6050C030 20 10 5 2 1 05 pl%l Q2 Ql Figure 5. Comparison of probability curves for river Wisla profile Hisla a 280 2U0 empirical curve / / confidence limits / / y 160 / y y' ^^ 120 y X --~"~~ y *?^ 80 >^ ^O" ^ *s ^u ^ * CO 1 n ' • ' • ' • * i i • • i ,• ' • • 100 99 90 807060SOi030 20 10 5 2 1 05 pl%l Q2 Ql Figure 6. Comparison of probability curves for river Hszanka profile Mszana Dolna 14 with confidence limits for a confidence level equal to 0.84. The Kolmogorow-Smirnowtes tgav esatisfactionar yresult sfo ral lcases . Next, theprobabilit y curveswer eestimate d again with theus eo f thedevelope d procedure,an ddisplaye do nfigure s3 t o6 fo rcompariso n with theempirica l ones. Thebes t agreemento fempirica l andsimulate d probabilitycurve swa sachieve dfo rth erive rWisl a (fig.5) , thewors t for Lesnianka river, (fig.3 )wher e mosto fth esimulate d curve falls outsideth econfidenc elimits .Ther ewasn' treasonabl eexplanatio nfoun d forthi sdiscrepancy . Table3 .Watershe ddescriptio nsummar yfo rmode levaluatio n Chanel No Watershed Profile Area Slope Forest length [km2] [km] [-] [%] 1 Lesnianka Lipowa 21.5 6.2 0.101 96 2 Lubierika Lubieri 46.9 11.1 0.032 42 3 Wisla Wisla 54.0 12.8 0.058 75 4 Mszanka MszanaDoln a 166.3 16.2 0.057 45 3.3.SENSITIVIT YANALYSI S The influence on flood flow magnitudes by arbitrary changes in parameter values hasbee n investigated inorde r toevaluat e themode l sensitivity. Three essential input characteristics have been tested: channel slope (I),annua l rainfall total (P),an dth eC N parametero f the SCS method. Parameter values have been changed by increasing and decreasing parameter values with 50%,20% , 15%, and 10%. Such an analysis was aimed to assess how far the parameter value errors influence flood flows.Th e second purpose was to assess, whether the model was flexible enough to reflect the influence of possible anthropogenicchange so nfloo dflows . The sensitivity analysis was carried out on the Wisla river catchment,whic hha dshow nth ebes tagreemen to fempirica lan dsimulate d 15 Figure7 .Result s ot sensitivityanalysi s lorWisl arive r flow probability curves.Th e analysis was performed for flows with an assumedprobabilit yo f1% .Th eresult so fth einvestigatio nar eshow ni n figure 7. The changes in channel slope show little influence on peak flow magnitude. The model ismor e sensitive to annual rainfall totals and isver ysensitiv et ochange s inC N parameter values.Thi sanalysi s shows importance of accurate evaluation of CN parameter value and satisfactory flexibility of the model to reflect the influence of possibleanthropogeni cchange si nth ewatershe do nfloo dflows . 3.4.SIMULATIO NEVALUATIO NO FPROBABILIT YCURVE SFO RANTHROPOGENI C CHANGES Humanactivit ycause sa variet yo fchange s inwatershed san dthei r environment and influences the flow regime. Among others, changes connected with urbanization, deforestation and modification of agricultural structure are most often observed. There were two cases analyzed for theWisl ariver : changes in forest quality (thecatchmen t 16 is for 75% covered by forest), and changes due to predicted climate changescause db yth eincreas eo fCO 2an dothe rradiativ etrac egase si n theatmosphere . Changes in forest covering is a very important factor in flood development.Althoug hrationa l natural resources management inmountai n areas will recommend tokee pa forest cover,predicte d changesconsis t ofdeterioratio no fth efores tcove rcause db yaci drain .Fou rdifferen t forest density levels werechose n for the assessment of the impact of thepredicte d changes. Itwa sdeal t with bymodifyin g theC N parameter value inth eeffectiv erai ndeterminatio n method. Partlydamage d forest was taken to be the actual condition. The average value of the CN parameter for this case was 83.2.Th e CN parameter values for heavily damaged forest, average density and dense forest were calculated according to theSC Smetho d and are given inTabl e 4. The probability curves for these three variants were calculated and they are shown in figure8 .Th enumber sdescribin gparticula rcurve stogethe r withth eC N parameter values for different forest densities and averages for the watershedar eshow ni nTabl e4 . As expected, the probability curves have been moved towards higher values for lower forest densities. The differences were bigger for the lowerprobabilities . Table4 .C Nparamete rvalue sfo rdifferen tfores tdensitie s Curvenumbe r Forestdensit y ForestC N AverageC N 1 actual 81 83.2 2 damaged 83 84.7 3 average 79 81.7 4 dense 77 80.2 Published forecastsconcernin g the influenceso fCC L concentration increaseo nclimat efactor sannounce ,tha tth eresultin g increasei nai r temperaturewoul dcaus ea n increase inévapotranspiratio nan drainfall , speeding up hydrologie processes (Mimikou et al 1991). The so-called 17 99 90 80 70 60 50 10 30 20 H} 5 2 1 05 p(K] 0.2 0.1 Figure 8. Probability curves comparison for different forest density 90 80 70 60 50 Iß 30 20 10 5 2 1 05 p/%/ 02 0.1 Figure 9. Probability curves comparison for different annual precipitation 18 GeneralCirculatio nModel s (Wilson,Mitchel l 1987)ar euse d forclimat e phenomena modeling. The most often made assumption is to double the atmosphericCO2 ,an di tresult si na nannua lprecipitatio n increasefro m 5%t o20 %(Arnel ,Reynar d 1983). Taking these results into account, three annual precipitation change scenarios were chosen for simulation computations: 5%, 10%an d 15% increase in the annual precipitation totals. The event rainfall depthswer eassumen dt o increasewit hthes esam epercentag e likeannua l totals. Three probability curves were calculated, they are shown in figure9 ,togethe rwit hth eactua lone .Thes ecurve sdescribe : 1 -actua lcurve , 2 -precipitatio nincreas eo f5% , 3 -precipitatio nincreas eo f10% , 4 -precipitatio nincreas eo f15% . 3.5.CONCLUSION S The proposed model for probability curves of flood flow computations aimso n evaluating theprobabl e flows fordesig n purposes in ungauged watersheds with the rainfall data from nearby standard weatherstations . Verification computations for the sub-models of the proposed procedure have shown satisfactory results incompariso n with empirical data. The developed model was tested with the use of empirically obtained probability curves for four small watersheds in theCarpatia n Mountains and it has shown to be acceptable. Sensitivity analysis has shown that themode l isabl et oreflec t influenceso fma n made changes onfloo dflo wmagnitude sb ymodifyin gth eappropriat eparameters . Two cases of changes caused by human activity were further evaluated with the model for the Wisla river. It concerns changes in forest cover quality and increase of annual precipitation due to the increase of CO2 inth e atmosphere. The model has shown its usefulness for thedescribe dcircumstances .Furthe r investigations arerecommende d for model verification in a greater number of watersheds, and for sub-modelrefinements . 19 REFERENCES ArnelN. ,N .Reynard ,1989 .Estimatin gth eimpact so fclimati cchang eo n river flows: some examples from Britain. Proc. of. Conf. on Climate andWater .Academ yo fFinland ,Helsinki ,pp .426-435 . Banasik,K. ,S . Ignar, 1986.Analysi so frainfal lduratio n influenceo n flood magnitude. Proceedings of the Int. Conf. "Hydrological Processes in the Catchment". Cracow Technical University, Cracow, pp.9-14 . Beran M.A., 1973. Estimation of design floods and the problem of equating theprobabilit yo frainfal lan drunoff . Int.Symp .o nDesig n of Water Resources Projects with Inadequate Data. IAHS, Madrid, pp.33-50 . Delleur, J.W., P.B.S. Sarma, A.R. Rao, 1973. Comparison of rainfall-runoffmodel sfo rurba nareas .Journa lo fHydrology ,vol .18 , no.3/4 ,pp .329-357 . Diskin M. H., 1974. A basic study of the linearity of the rainfall-runoffproces si nwatersheds .Thesis ,Universit yo fIllinois , Urbana.p .87 . DVWK, 1984. Regeln zur Wasserwirtschaff. Heft 113. Teil II,Synthese . VerlagPau lParey ,Hambur g- Berlin,p .34 . Hawkins R.H., A.T . Hjelmfelt, A.W. Zevenberger, 1985. Runoff probability, storm depth and Curve Numbers. Journal of Irrigation andDrainage ,vol .Ill ,no .4 ,pp .330-340 . Ignar, S., 1986. An example of a rainfall-runoff model for design floodcomputations .Wageninge n Agricultural University.Departmento f Hydraulicsan dCatchmen tHydrology .Repor tno .74 .p .26 . Ignar, S., S. Weglarczyk, 1991. Statistical computations package for PC/AT.Use rguide , (inPolish) .Manuscript ,p .14 . MimikouM. ,Y. ,Kouvopoulo sY. ,G. ,Cavadia sN .Vayianos . 1991.Regiona l hydrological effects of climate change. Journal of Hydrology, vol. 123,no .1 ,pp .119-146 . National Engineering Handbook, 1985. Soil Conservation Service, Sect.4,Hydrology ,USDA .Washingto nD.C .pp .10.1-10.24 . RaudkiviA.J. ,1979 .Hydrology .A nadvance d introductiont ohydrologica l processesan dmodelling .Pergamo nPress .Oxford ,pp .118-125 . Stachy J., 1976. Application of rational formula for maximal flows computation insmal lungauge dwatershed , (inPolish) . Wiad.Met .i Gosp.Wod. ,vol .Ill ,pp .53-70 . Wilson CA., J.F.B. Mitchell, 1987.Simulate d climate and COa induced climate change over western Europe. Climatic Change, vol. 10, pp. 11-42. 20